Members of the Hedgehog family of signaling molecules mediate many important short- and long-range patterning processes during invertebrate and vertebrate development. Genetic and functional studies demonstrate that patched is part of the hedgehog signaling cascade, an evolutionarily conserved pathway that regulates expression of a number of downstream genes. In addition to embryonic development and patterning, hedgehog signalling has been implicated in wound healing, hair growth, nerve repair, angiogenesis, and other processes in adult organisms. Accordingly, methods and compositions for modulating differentiation or proliferation of cells, particularly using small molecules that are simpler to administer than a peptide, would be useful.